On dynamics of quadratic stochastic operators generated by 3-partition on countable state space

Karim, Siti Nurlaili and Hamzah, Nur Zatul Akmar (2024) On dynamics of quadratic stochastic operators generated by 3-partition on countable state space. Communications Faculty of Sciences University of Ankara-Series A1 Mathematics And Statistics, 73 (4). pp. 1114-1133. ISSN 1303-5991 E-ISSN 2618-6470

PDF - Published Version Restricted to Repository staff only Download (633kB) | Request a copy

Abstract

Quadratic stochastic operator (QSO) theory has advanced significantly since the early 1920s and is still growing due to its numerous applications in a variety of fields, particularly mathematics, where QSOs have inspired mathematicians to use and integrate various mathematical knowledge and concepts to better understand their properties and behaviors. Motivated by the relationship between the number of partitions on an infinite state space and the development of the system of equations corresponding to QSOs, this work sought to investigate the dynamics of QSOs formed by three partitions. First, we define and construct the 3-partition QSOs, which result in a system of equations with three variables. We then provide the formulation of the fixed point form and discuss its behavior using Jacobian matrix analysis. Some scenarios of three-partition QSOs with three different parameters are considered to readily investigate the type of fixed point in such systems. It is demonstrated that the operators can have either an attracting or a saddle fixed point but can never be repelling. We show how the saddle fixed point behaves, by identifying a set of points known as the fixed point’s stable manifold.

Item Type:	Article (Journal)
Uncontrolled Keywords:	Dynamical system, Fixed Point, System of Equations
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA300 Analysis
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences Kulliyyah of Science
Depositing User:	Nur Zatul Akmar Hamzah
Date Deposited:	03 Jan 2025 15:10
Last Modified:	03 Jan 2025 15:10
URI:	http://irep.iium.edu.my/id/eprint/117706

Actions (login required)

View Item